At first glance it looks like just another cycle shop, albeit a slightly posh west London one, stocking a mix of sturdy commuter machines, mountain bikes, small-wheeled folding ones, even a tandem. But a closer look reveals the boxy battery packs attached to frames or luggage racks. These are e-bikes, and proponents say they could change urban transport forever.

Electrically assisted bikes, the sort that can be used without a licence or insurance if they stay within certain power and speed restrictions, remain relatively rare in Britain, but elsewhere in Europe they are increasingly big business.

Last year 310,000 e-bikes were sold in Germany, a 55% year-on-year rise. In all more than 700,000 were sold in western Europe. The equivalent figure for electric cars, long touted as the low-carbon transport of the future, was just over 11,500, even with the millions spent on subsidies and on-street charging points.

The UK saw a relatively paltry 20,000 e-bike sales last year, but supporters hope the electric bike could help overcome the longstanding British resistance to cycling as everyday transport. E-bikes, they argue, which provide a smooth but significant extra kick when the pedals are turned, allow people of more or less any age or fitness level to whirr smoothly from place to place, even up steep slopes, arriving unflustered and un-sweaty. This is particularly valuable, they add, in an era of ageing populations.

"You travel faster for less effort – who can argue with that?" says James FitzGerald, whose Suffolk-based Justebikes company has just opened the west London store, its first in the capital. "They're also safer for city cycling as the added acceleration means e-bike riders can move away from traffic lights more quickly. And in a city they're much more practical than an electric car." E-bikes, also known as electronically power assisted cycles (Epacs) or pedelecs, certainly seem to have a wide demographic appeal compared with regular bikes – a survey by the British Electric Bicycle Association found more than a third of purchasers were aged 50-59.

While the most common models tend to be commuter bikes, in FitzGerald's shop are folding models and electric mountain bikes, often bought by outdoor enthusiasts with ageing limbs or creaking knees. There is even an electrically assisted bakfiets, the traditional Dutch-style cargo cycle with a container at the front big enough for a couple of children and a weekly shop, the manual versions of which can require iron thighs for the slightest incline.

E-bike technology has moved on considerably from slightly clunky early incarnations. Batteries are lighter and longer-lasting, while the Dutch-made Sparta brand sold by FitzGerald features such gizmos as an electronic speed and power display which doubles as an immobilser - take it off the bike and the motor cannot be used.

FitzGerald says he has held talks with Norman Baker, the Liberal Democrat junior transport minister and semi-official voice of cycling in the government, over ways to increase the take-up for e-bikes, while the Department for Transport says it sees e-bikes as a potentially important part of wider strategies to get people on bikes.

It nonetheless remains uncertain whether they will take off in the UK, with its lack of a wider cycling culture: overall, the percentage of journeys made by bike every year is around 2%, against more than 25% in the Netherlands. The European Cyclists' Federation says Britons are little more likely to ride an e-bike than a normal bike if they feel the lack of dedicated bike lanes and other infrastructure makes it unsafe. E-bikes can also seem expensive to Britons unused to buying good-quality bikes: the well-made Sparta bikes sold by FitzGerald start at around £1,500.

Carlton Reid, editor of the BikeBiz cycle industry website, predicts that such factors will limit the growth of e-bikes in countries like the UK and US.

"There's no sign that e-bike sales in the UK are about to sky rocket," he predicts. "Because of its cycling infrastructure, the Netherlands has a ready market for bicycles and when Dutch cycle shop customers get older they naturally gravitate towards power assistance. Very importantly, the average selling price of a Dutch roadster is far above the average selling price of a standard bike in Britain. And Brits are not used to paying £1,000 for their bikes, so bikes that cost more than this are scary, scary expensive."

What is an e-bike?

The point at which an e-bike becomes an electric moped, and thus subject to all sorts of laws about helmets, insurance and licences, is somewhat complex and covered by a range of EU regulations.

In the simplest terms, an e-bike must weight less than 40kg, have a power output of no more than 200w and must propel you to no more than 25kph, or just over 15mph. Crucially, they must (at least officially) only offer electric assistance, meaning the pedals have to turn for the motor to kick in even if there is a separate throttle.

In practice, put one of the modern machines on the top power setting and it will whizz you from a standing start to 15mph with the barest spin of the pedals. Some e-bikes come with a boost button taking them over 15mph, labelled with an unspoken wink as "off-road use only". This is most likely not legal, the DfT warns. Riders of any e-bike have to be aged over 14.